Time-dependent Neutral stochastic functional differential equation driven by a fractional Brownian motion in a Hilbert space

TL;DR

This paper establishes existence and uniqueness of solutions for a class of time-dependent neutral stochastic functional differential equations driven by fractional Brownian motion in a Hilbert space, using fixed point methods.

Contribution

It introduces a novel framework for analyzing such equations with fractional noise and provides a practical example demonstrating the applicability of the theoretical results.

Findings

Proved existence and uniqueness of mild solutions.

Applied Banach fixed point principle to stochastic equations.

Provided a practical example illustrating the theory.

Abstract

In this paper we consider a class of time-dependent neutral stochastic functional differential equations with finite delay driven by a fractional Brownian motion in a Hilbert space. We prove an existence and uniqueness result for the mild solution by means of the Banach fixed point principle. A practical example is provided to illustrate the viability of the abstract result of this work.